Data-driven resource allocation for multi-target attainment

We delve into a class of multi-target attainment problems, which commonly arise in practical applications such as operations management, marketing, policy making, and healthcare services. The aim is to efficiently allocate a fixed amount of resources to achieve predetermined target payoffs for multiple tasks. We transform this stochastic problem into a tractable optimization problem that, when optimized, approximately maximizes the probability of attaining all the targets as data accumulates. This transformation is leveraged to devise a batch-based resource allocation rule that demonstrates strong theoretical and numerical performance guarantees.